Answer:
The wavelength of the light is [tex]5.9*10^{-7}m[/tex].
Explanation:
The band separation [tex]\Delta y[/tex] for a light wave of wavelength [tex]\lambda[/tex] is given by
[tex]\Delta y = \dfrac{\lambda L}{d},[/tex]
where [tex]d[/tex] is the slit separation, and [tex]L[/tex] is the distance to the screen.
Solving the above equation of wavelength [tex]\lambda[/tex] we get:
[tex]\lambda = \dfrac{\Delta y \:d}{L}.[/tex]
Now, in our case
[tex]\Delta y = 3.9*10^{-4}m[/tex]
[tex]d= 3.0*10^{-3}m[/tex],
and [tex]L = 2.0m[/tex];
therefore,
[tex]\lambda = \dfrac{3.9*10^{-4}m *3.0*0^{-3}m}{2.0m}.[/tex]
[tex]\boxed{\lambda = 5.9*10^{-7}m,}[/tex]
which is the 2nd choice from the options given.
